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Based on Lyapunov stability theory, matrix analysis method, linear matrix inequality methods, etc, the generalized H2 control of singularly perturbed uncertain control systems with time-varying delay and control input and disturbance input is studied. A memory state H2 generalized controller is designed, the decision theorem of the specific design method given. Quoting new lemma for delay dependent and delay independent cases, the relatively less conservative stability criterion is derived. The obtained results are linearized, the selected numerical examples are used to verify the effectiveness and feasibility to the derived conclusions. It is pointed out that the closed-loop system is asymptotically stable in the whole range from zero to singular perturbation upper bound, which expands the generalized H2 stability space and reduces the L2-L performance index. By comparing the stability state parameter index with the related literatures, it is shown that the proposed method has certain advantages and less conservatism, and is suitable for standard and non-standard cases.
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A Mindlin plate theory for micro-nano structures is proposed based on couple stress theory. A length scale parameter was introduced to take into account the scale effect and the constitutive equations of the micro-nano Mindlin plate were derived by considering the transverse shear deformation. The governing equations in terms of displacements and the slope functions of buckling and free vibration for shear deformation micro-nano plate were further deduced from force equilibrium conditions. The analytical solutions of buckling and free vibration for shear deformation micro-nano plate were obtained by separating the displacement and rotation variables in space and time domains. Two scenarios of boundary conditions were analyzed: SSSS (simply supported by four edges) and SCSC (two opposite edges simply supported and other two edges clamped). A MATLAB program was developed to compute the critical buckling and natural frequency with different value of scale ratio, aspect ratio and length-to-thickness ratio. The theoretical solutions are compared with the results from ABAQUS finite element analysis and the predictions obtained from existing studies and found in good agreement with the other two methods. The results show that the scale effect has a significant effect on the buckling load and the natural frequency.
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In order to improve the efficiency of stochastic model updating and reduce the amount of calculation, a stochastic model updating method based on Kriging model and lifting wavelet transform is proposed. Firstly, perform lifting wavelet transform on the acceleration frequency response function, and extract the fifth-level approximate coefficients to replace the original frequency response function; secondly, use the Latin hypercube sampling to sample the parameters to be updated and the corresponding approximate coefficients as the outputs to build the Kriging model. A butterfly optimization algorithm with the Lévy flight (LBOA) is proposed and use to improve the accuracy of the Kriging model; finally, with the goal of minimizing the Wasserstein distance, the mean value of the parameters to be updated is solved by the whale optimization algorithm. The results of the test function show that LBOA has greatly improved in terms of optimization, convergence accuracy and stability. The updating errors of the numerical examples are all less than 0.4%, verifying that the proposed model updating method has high accuracy and efficiency.
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The sine-cosine method is applied to the wave equation of nonlinear elastic rod, and some new periodic and soliton solutions of the equation is obtained (material constant n is a constant different from 1). The graphs of some solutions are given through math software. The results are helpful to further research on existence of solitary waves in the nonlinear elastic rod.
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The flow boiling phenomenon in a channel with multiple rectangular heaters under constant wall temperature was numerically studied by lattice Boltzmann method. The effects of distance between/among heater, heater length and heater surface wettability on bubble morphology, bubble area and heat flux of the heater surface were studied. The results show that the bubble growth rate increases with the increase of the distance between/among heaters, the larger bubble area promotes the nucleated bubbles to leave the heater surface in advance, and the corresponding boiling heat transfer performance increases by 12% with the increase of the distance between/among heaters from 250 lattices to 1000 lattices. On the other hand, the longer the heater length, the earlier the bubble nucleation time and separation time from the heater surface, and the better the boiling heat transfer performance, and the boiling heat transfer performance increases by 13% with the increase of the heater length from 16 lattices to 22 lattices. In addition, the bubble nucleation time of the hydrophilic surface is later than that of the hydrophobic surface. Compared with the hydrophilic surface, there are residual bubbles on the hydrophobic surface after the bubbles leave the heater. The average heat flux and bubble area of hydrophilic surface are less than those of hydrophobic surface. When the contact Angle changes from 77° to 120°, the heat transfer performance increases by 26%. Finally, through the orthogonal test scheme, it is found that the wettability of the heat exchanger surface has the greatest influence on the flow boiling heat transfer performance, while the heater length has the least influence on the flow boiling heat transfer performance.
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The sampling consensus of second-order multi-agent systems with time-varying topology is investigated based on the constant position difference and consistent speed. Firstly, the virtual leader is introduced and the sampling consensus problem of multi-agent systems is transformed into the stability problem of the corresponding error system. Secondly, by estimating the sampling error, the influence of sampling error on system consistency is studied. Finally, by virtue of the Lyapunov stability theory, the stability of the constructed error system is analyzed, and a sufficient condition for the stability of the error system is given. The numerical simulation results verify the effectiveness and correctness of the theoretical analysis.
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In the case of Reynolds number Re=3000 ~ 50000, Stokes number St=0.1 ~ 10, Dean number De=1400 ~ 2800, the orientation and deposition characteristics of cylindrical particles with aspect ratio β=2 ~ 12 in a turbulent flow through a curved tube are studied. The motion of cylindrical particles is described by the slender body theory combined with the Newton's second law. The orientation distribution function of cylindrical particles is given by the Fokker Planck equation. The mean velocity of the flow is obtained by solving the Reynolds-averaged Navier-Stokes equation and Reynolds stress equation. The turbulent fluctuating velocity acting on particles is described by the kinetic simulation sweeping model. By solving the equations of turbulent flow and particle motion and orientation distribution function, the orientation distribution of particles on the cross-section at different axial positions and outlet is obtained and analyzed. The effects of various parameters on the deposition rate of particles are discussed. The results showed that the main axis of particles tends to the flow direction with the increase of St and β, and the decrease of De and Re. Deposition rate of particles increases with increasing De, Re and β. However, it shows a non monotonic trend with the change of St. Conclusion has reference value for practical engineering application.
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For the transverse vibration of slightly curved pipe, a dynamic mechanical model based on Timoshenko beam theory is established for the first time. The natural vibration characteristic of slightly curved pipe under the influence of the fluid flow is analyzed. With generalized Hamiltonian principle, the governing equation of the transverse vibration of slightly curved pipe considering the effect of fluid-structure coupling is derived. Based on Galerkin truncation, the natural frequencies of slightly curved pipe are obtained by generalized eigenvalue method. Effects of the fluid velocity and the initial deflection on the natural vibration characteristic of the pipe are studied. The equivalent stiffness and equivalent damping method base on finite element simulation for the natural vibration of the slightly curved pipe are developed. Then through the finite element numerical simulation software, the results of Galerkin truncation method and the effectiveness of the Timoshenko model are verified. The results show that fluid velocity and the initial bending degree both have significant effects on the natural frequencies of slightly curved pipe.
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In order to meet the requirement of high accuracy and high resolution in computational fluid dynamics (CFD), a new reference smoothness indicator is proposed to reduce the numerical dissipation of the classical third-order weighted essentially non-oscillatory (WENO) scheme.Its construction method is different from the classical WENO-Z scheme. It is obtained by the $L^2$-norm approximation of the linear combination of the derivatives of the reconstruction polynomials of the candidate sub-stencils and the derivatives of the reconstruction polynomials of the whole global stencil.Using this calculation method, higher-order reference smoothness indicators can be obtained than WENO-Z scheme. In addition, different reference smoothness indicators can be obtained by changing the value of free parameter $\varphi$. The effectiveness of the reference smoothness indicator is proved by a series of numerical examples.
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2022, Volume 43, Issue 6 publish date：June 01 2022
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2022, 43(6): 597-607.   doi: 10.21656/1000-0887.420326
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The circular membrane solar array has attracted extensive attention due to its high storage ratio and strong power supply capability. In order to adjust the tension of large film structures, a tension adjusting device composed of ropes and springs is usually introduced, and its mechanical characteristics are highly nonlinear, with the effects rarely studied yet. Aimed at the tension adjustment, a mechanism model was proposed. The nonlinear dynamics equation for the 2DOF system was established with the Lagrangian energy method. With an engineering prototype as the example, the responses of the tension mechanism with unsymmetrical ribs under resonance excitation were studied. The results show that, the change of the excitation amplitude has an important influence on the characteristics of the beat response of the system. Consequently, the responses of the system exhibit chaotic, almost periodic and multifold periodic phenomena. The research makes an important reference to the parameter design of tension mechanisms.

2022, 43(6): 608-618.   doi: 10.21656/1000-0887.420295
Abstract(121) HTML(46) PDF(35)
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The radial basis function partition of unity (RBF-PU) method  was applied to obtain the numerical solution of 2D nonlocal diffusion and peridynamic problems. The main idea is to partition the original domain into several patches, use the RBF approximation on each local domain, and then give weighting to obtain the global approximation of the unknown function. The radial basis function method based on the strong form of the equation has many advantages, such as avoiding an additional layer of integral calculation, no need to deal with intersections of neighborhoods with the mesh, and easiness of implementation. The numerical results show that, this method can solve nonlocal diffusion equations and peridynamic equations accurately and efficiently.

2022, 43(6): 619-630.   doi: 10.21656/1000-0887.420177
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The grazing-induced non-smooth dynamical behaviors of single-degree-of-freedom cantilever beam systems with bilateral elastic constraints were studied. Firstly, based on the dynamical equations for the cantilever beam under elastic impacts and the definition of grazing points, the existence condition for the bilateral grazing periodic motion was analyzed. Secondly, the zero-velocity Poincaré section was selected to derive the high-order discontinuous mapping with parameters near bilateral grazing orbits. Then a new composite piecewise normal form mapping was established through combination of the smooth flow mapping and the high-order discontinuous mapping. Finally, the validity of the high-order mapping was verified through comparison of the bifurcation diagram of the low-order mapping with that of the high-order mapping, and the grazing dynamics of the cantilever beam under elastic impacts were further revealed through numerical simulation.

2022, 43(6): 631-638.   doi: 10.21656/1000-0887.420353
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The superconducting thin film is a kind of multilayer structure prepared by chemical coating. As a conductive functional structure material with excellent performance, its structural integrity is directly related to the current-carrying capacity. During the preparation of superconducting thin films, it is hard to avoid the interface cracks between the superconducting layer and the metal substrate. In this case, along with the current-carrying operation, the strength of the interface crack in an external magnetic field makes a key problem. Therefore, based on the theory of flux through the thin film and the linear elastic fracture, an analytical model was established for the strength of the interface crack between the superconducting film and the substrate. The effects of the viscous flux flow on the stress field and the energy release rate at the crack tip were obtained. The results show that, the higher the flux flow velocity is, the greater the stress and the energy release rate at the crack tip of the interface will be, which will lead to crack propagation along the interface. The work is helpful for the analysis of interface cracks mentioned above.

2022, 43(6): 639-647.   doi: 10.21656/1000-0887.420202
Abstract(44) HTML(25) PDF(12)
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The anti-plane problem of asymmetric collinear interface cracks emanating from a circular hole in 1D hexagonal quasicrystal bi-materials was studied. With the Stroh formula and the complex function method, the complex potential functions under the coupling action of the phonon field and the phason field were obtained. The analytical expressions of the stress intensity factor (SIF) and the energy release rate (ERR) at the crack tip were given. The effects of the circular hole radius and the crack length on the SIF, and the effects of the coupling coefficient, the phonon field stress and the phason field stress on the ERR, were discussed. The results show that, the SIF tends to be stable with the increase of the right crack length for a constant circular hole radius. For a certain phason field stress value, the ERR reaches the minimum value, which indicates that a specific phason field stress can inhibit the crack growth.

2022, 43(6): 648-659.   doi: 10.21656/1000-0887.420206
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The vibration suppression performance of a damping composite structure depends on the material layout and the damping material properties. A topology optimization method was proposed for damping material microstructures with varied volume constraints, to obtain the damping material microstructure with desired properties under the smallest material consumption. Based on the homogenization method, a 3D finite element model for the damping material was established, and the effective elastic matrix of the damping material was formulated. The Hashin-Shtrikman bounds theory was used inversely to estimate the volume fraction bound of the damping material corresponding to the desired effective modulus, and a movement criterion for volume constraint bounds of damping materials was constructed. Then the optimization problem of achieving the desired properties of damping materials with microstructures was converted to another problem of maximizing the desired modulus under volume constraints, and a topology optimization model for the damping material microstructure was established. The optimality criteria method was employed to update the design variables, and the optimized topology configurations of damping material microstructures were obtained. The feasibility and effectiveness of the proposed method were verified with several numerical examples, and the influences of the initial configurations, the mesh density and Young’s modulus on the microstructure configurations of the damping material were also discussed.

2022, 43(6): 660-668.   doi: 10.21656/1000-0887.420150
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The peridynamic differential operator (PDDO) theory was introduced to solve the 2D transient heat conduction problems. The heat conduction equation and the boundary condition were reformulated from the local differential form to the non-local integral form. Then the Lagrangian multiplier method and the variational analysis were used, and a non-local model for 2D transient heat conduction problems was established. Through error and convergence analysis, the accuracy of this model was verified in comparison with the results of other numerical methods. The model was further applied to solve the 2D transient heat conduction problems of plates with irregular boundaries and micro-defects (cracks and holes). The results show high accuracy, wide applicability and good convergence of this method, which provides new insights into the 2D transient heat conduction problems.

2022, 43(6): 669-681.   doi: 10.21656/1000-0887.420190
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Aimed at the phenomenon of competing for water resources between young vegetation and adult vegetation in arid and semi-arid areas, a vegetation-soil water dynamic model with intraspecfic competition delay was established. The conditions for the existence of an unique vegetation survival equilibrium and the local stability of the vegetation extinction equilibrium were analyzed. The generating conditions for Hopf bifurcating periodic solutions of non-spatial and spatial systems were given, respectively. The periodic oscillation pattern appearing in the vegetation evolution with time was numerically simulated. Through the parameter sensitivity analysis, the rainfall and the vegetation growth rate were found to have significant influences on the generation, the amplitude and the period of this pattern, while the effects of evaporation was found to be the least significant. The results indicate that, the rainfall and the vegetation properties have profound impacts on the evolution and development of vegetation in arid and semi-arid areas. The introduction of spatial diffusion inhibits the occurrence of this pattern, but doesn’t affect the amplitude and the period. The work explains the phenomenon of vegetation periodic oscillation widely observed in nature, and provides theoretical supports for the sustainable development of the vegetation system.

2022, 43(6): 682-689.   doi: 10.21656/1000-0887.420248
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A class of multi-objective fractional semi-infinite optimization problems with uncertain data were investigated. Firstly, a robust optimization model corresponding to the uncertain multi-objective optimization problem was introduced. Then the optimization model was converted to a multi-objective optimization problem with the Dinkelbach method. In turn, by means of the scalarization method, the corresponding scalarization optimization problem was built, and the relationship between robust solutions to the multi-objective optimization problem and its corresponding scalarization optimization problem was described. Finally, through a robust-type sub-differential constraint qualification, the robust optimality condition for approximate quasi-efficient solutions to the multi-objective fractional optimization problem was established.

2022, 43(6): 690-699.   doi: 10.21656/1000-0887.430009
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Based on the deterministic network infectious disease model, a stochastic network infectious disease model under the influence of white noise was established, and the existence and uniqueness of the global solution to the model were proved. With the theory of stochastic differential equations, sufficient conditions for stochastic extinction and persistence of infectious diseases were obtained. The results show that, white noise has a great impact on the transmission dynamics of network infectious diseases. White noise can effectively suppress the spread of infectious diseases, and large white noise can even make the original persistent infectious diseases become extinct. Finally, the theoretical results were verified through numerical simulations.

2022, 43(6): 700-706.   doi: 10.21656/1000-0887.420183
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With the central difference scheme to discretize the Riemann-Liouville time fractional derivatives and by means of the finite point method to establish discrete algebraic equation systems, a meshless finite point method was proposed for the numerical analysis of the fractional Cable equation. The error estimation of the method was derived and discussed in detail. Numerical examples verify the efficiency and convergence of the method and confirm the theoretical results.

2016, 37(2): 149-159.   doi: 10.3879/j.issn.1000-0887.2016.02.004
[Abstract](1142) [PDF 5386KB](734)

2017, 38(1): 1-31.   doi: 10.21656/1000-0887.370578
[Abstract](1192) [PDF 1039KB](1418)

《随机振动的虚拟激励法》自1985年正式发表以来，逐渐得到许多工程领域的认可和采用，解决了很多重要而困难的工程问题.该方法不但被国内某些工程规范所推荐，而且被3种国际工程手册成章刊载，在国际上亦占有了一席之地.该文是笔者参考了数百篇国内外论文，依据其中一部分在11个工程领域对虚拟激励法的应用和一些学者的评论所撰写的综述.借以让更多工程技术人员和研究者对虚拟激励法有较为全面的了解，以结合各自工程领域更有效地开展对随机振动理论和方法研究成果的应用和发展.
2017, 38(1): 44-59.   doi: 10.21656/1000-0887.370571
[Abstract](1094) [PDF 647KB](944)

2020, 41(3): 339-352.   doi: 10.21656/1000-0887.400176
[Abstract](699) [FullText HTML](76) [PDF 405KB](288)

2016, 37(12): 1272-1281.   doi: 10.21656/1000-0887.370546
[Abstract](797) [PDF 3862KB](611)

2017, 38(1): 32-43.   doi: 10.21656/1000-0887.370336
[Abstract](1143) [PDF 683KB](2049)

2016, 37(1): 73-83.   doi: 10.3879/j.issn.1000-0887.2016.01.006
[Abstract](985) [PDF 1871KB](684)

2016, 37(8): 791-803.   doi: 10.21656/1000-0887.370056
[Abstract](812) [PDF 589KB](827)

2017, 38(4): 369-398.   doi: 10.21656/1000-0887.370328
[Abstract](1225) [PDF 6800KB](1183)

2016, 37(12): 1345-1358.   doi: 10.21656/1000-0887.370525
[Abstract](1130) [PDF 3993KB](551)

2008, 29(8): 947-953.
[Abstract](2993) [PDF 460KB](21)
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A study of double dissintilar orthotropic composite materials interfacial crack was made by constivcting new stress functions and employing the method of composite material complex.In the case that the characteristic equations' discriminants are all more than zero,the theoretical fonmula of the stress field and the displacement field near the mode Ⅰ interface crack tip,without oscillation and inter-embedding between the interfaces of the crack were delved.
2002, 23(5): 441-451.
[Abstract](5572) [PDF 395KB](119)
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The solution and computational aspects on nonlinear deflection of Yongjiang Railway Bridge in Ningbo were investigated.An approximate iteration algorithm on nonlinear governing equation was presented,and the obtained results show that,if altitude difference and span of the riverbanks are taken as 5 meters and 100 meters,respectively,the maximum gradient in the middle of the bridge exceeds 5%,much larger than maximum allowance gradient in railway design code.Therefor,a new solution scheme for decreasing gradient of the bridge is put forward,that is,the altitude difference between two riverbanks can be decreased to about 1/10 of the initial magnitude by building roadbeds with 0.5% gradient and 1 kilometer length at two riverbanks.As a direct result,the deflection gradient of the railway bridge is much reduced and the value is between 0.5%~0.6%.
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Founded in 1980 ( monthly )

Supervisor：Chongqing Jiaotong University

Founder：CHIEN Weizang

Honorary Chief Editor：ZHONG Wanxie

Editor-in-Chief：LU Tianjian

ISSN 1000-0887

CN 50-1060/O3